Can I skip my period while on birth control?

I started a new pack of birth control during the week I should've had my period and taken the inactive pills. I started the active pills 2 days after my period was supposed to start. I had cramping and light bleeding in the beginning but I successfully stopped the bleeding. Is this safe to do? I haven't used a condom while having sex during this process. Does this effect my chances on getting or being pregnant?